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The function f(x) = x^3 - 3x + 2 is differentiable at x = 1?

Practice Questions

Q1
The function f(x) = x^3 - 3x + 2 is differentiable at x = 1?
  1. Yes
  2. No
  3. Only left
  4. Only right

Questions & Step-by-Step Solutions

The function f(x) = x^3 - 3x + 2 is differentiable at x = 1?
  • Step 1: Identify the function f(x) = x^3 - 3x + 2.
  • Step 2: Recognize that f(x) is a polynomial function.
  • Step 3: Understand that polynomial functions are smooth and continuous.
  • Step 4: Know that smooth and continuous functions are differentiable everywhere.
  • Step 5: Conclude that since f(x) is a polynomial, it is differentiable at x = 1.
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